Exact Solutions of Simple Nonlinear Difference Equation Systems that show Chaotic Behavior

Abstract

Abstract Exact solutions are given for May's simple difference equation and the broken linear model, both for extreme values of the parameters, and the relation between these two systems for the solvable cases is clarified. The invariant measure and the correlation function for each case are calculated using the exact solutions. The initial-value dependence of the behavior of the solutions, choatic or periodic, is completely determined. By using the exact solution, encounters of any two nonperiodic orbits can be precisely analyzed.